Separation axioms in L-fuzzy topological spaces (I): T0 and T1

doi:10.1016/S0165-0114(98)00431-X

Fuzzy Sets and Systems

Volume 116, Issue 3, 16 December 2000, Pages 377-383

https://doi.org/10.1016/S0165-0114(98)00431-X Get rights and content

Abstract

Using the notion of remote neighborhood, we define the separation axioms $T_{0}$ and $T_{1}$ in $L$ -fuzzy topological spaces ( $L$ -fts). The relations between our definitions, Hutton and Reilly's, and Wang's are discussed, and the separations of Hutton's fuzzy unit interval and Gantner's fuzzy real line are examined. Characterizations of these $L$ -fts are proved and a series of properties of them are investigated. Moreover, some results on minimal $T_{0} L$ -fts and $T_{1} L$ -fts are established, which will be used immediately in our subsequent discussion.

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^☆: This work was supported by the National Natural Science Foundation of China (Grant No. 19701020) and the Provincial Natural Science Foundation of Shaanxi.

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Separation axioms in L-fuzzy topological spaces (I): T0 and T1☆

Abstract

J. Math. Anal. Appl.

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

J. Math. Anal. Appl.

A Compendium of Continuous Lattices

Probabilistsche Metriken auf der Menge nicht negativen Verteilungsfunktionen

Aequationes Math.

Separation axioms in $L$ -fuzzy topological spaces (I): $T_{0}$ and $T_{1}$ ☆